fa یک میدان برداری هندسی جدید و کاربرد آن در نسبیت عام هندسه دیفرانسیل Differential Geometry علمی پژوهشی بنیادی S <span dir="RTL" lang="FA" style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">یک سالیتون هذلولوی یک منیفلد شبه-ریمانی</span></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>(</m:r></span></span><i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>M</m:r></span></span></i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>,</m:r></span></span><i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>g</m:r></span></span></i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)</m:r></span></span> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:2.5pt"><img alt="" src="data:image/png;base64,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" style="width:43px; height:18px" ></span></span></span></span><span style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">&nbsp;به همراه یک میدان برداری </span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>X</m:r><m:r>&isin;</m:r></span></span></i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="p"></m:sty></m:scr></m:rpr>X</m:r></span></span><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="p"></m:sty></m:scr></m:rpr>(</m:r></span></span><i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>M</m:r></span></span></i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)</m:r></span></span> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:2.5pt"><img alt="" src="data:image/png;base64,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" style="width:70px; height:18px" ></span></span></span></span><span style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">&nbsp;و اسکالرهای </span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>&mu;</m:r></span></span></i> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:2.5pt"><img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAXCAIAAACwBjnoAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAALxJREFUOE/tksERwiAQRRdqUQ8ZK4A+LCEU4yVcLcFTLoYOqMDJQegF2UUCjJlhvLuXzEt+Pn9/wkII0BveE+Dzv+jHCoxiTGqfu/VaFs5lmvkGcD4dssittvBH5F9PADEcN6OW4wcOwU0iaiZH8M3JqTHf4e3FcWl8oHBAJ/+42yqQuUasA1JPdJhdHeqNkvNwiQlxvFaplJRaCLovRgpPeyAtaRVImrJYDlZfOR1Wtbj3O3OqujMcq+3NG23KmxTJbefAAAAAAElFTkSuQmCC" style="width:10px; height:18px" ></span></span></span></span><span style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">&nbsp;و </span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>&lambda;</m:r></span></span></i> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:2.5pt"><img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAXCAIAAABS2iKRAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAKtJREFUOE9j/P//PwNewIRfGihLfxV3JqZbM4KA9cQ7SM4D+gUCtqVZpW27/f//7QlWDAxp2+DiDHAWnAFSgqQCi19U1HSQg4Ac325P95qFzwx0ebQwvTPR2muW1YQJaTjMuDMxvuCY1YSF3gxXUCIL5klwMIB9id23YP1A+ZmeGHEN9i0eeaAsKLhBqhChCLLFasJtoG1pIEEGdHmguyBOskoDqgICxkGSCgH8zZx1MjOp6wAAAABJRU5ErkJggg==" style="width:9px; height:18px" ></span></span></span></span><span style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">&nbsp;است که در تساوی</span></span><br> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>R</m:r></span></span><i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>ic</m:r></span></span><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>+</m:r></span></span><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>&lambda;</m:r></span></span></i> <span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="p"></m:sty></m:scr></m:rpr>L</m:r></span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>X</m:r></span></span></i> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>g</m:r></span></span><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>+</m:r></span></span></i> <span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>1</m:r></span></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>2</m:r></span></span> <span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="p"></m:sty></m:scr></m:rpr>L</m:r></span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>X</m:r></span></span></i> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>(</m:r></span></span> <span cambria="" math="" style="font-family:"><m:ctrlpr></m:ctrlpr></span> <span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="script"><m:sty m:val="p"></m:sty></m:scr></m:rpr>L</m:r></span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>X</m:r></span></span></i> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>g</m:r></span></span></i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>)=</m:r></span></span><i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>&mu;g</m:r></span></span></i> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:6.0pt"><img alt="" src="data:image/png;base64,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" style="width:206px; height:27px" ></span></span></span></span><span style="font-size:12.0pt"><span niloofar="" style="font-family:" xb="">&nbsp;صدق می‌کند. میدان برداری </span></span> <i><span style="font-size:12.0pt"><span cambria="" math="" style="font-family:"><m:r>X</m:r></span></span></i> <span style="font-size:12.0pt"><span calibri="" style="font-family:"><span style="position:relative"><span style="top:2.5pt"><img alt="" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAXCAIAAABfxFLWAAAAAXNSR0IArs4c6QAAAAlwSFlzAAASdAAAEnQB3mYfeAAAAJtJREFUOE/NkrEVACEIQ/XGYiDncRqXcRgPEBC0sdSSFz4JmMcY6eJ9FxqSvK5LmJder2CJSuNSK66iOquX2qVVlUAVp5tMgSmQRbRja9bhIqQmWE1BN4mEIG+OvPEkDgCinM1jruUOqNMfj0PYNnPjsXPxFs35vM45L3gbPfO2EpyzMCZB3TxZ6D+FSe+6dtqJzg9resT8+L//AbNLd2inAHmXAAAAAElFTkSuQmCC" style="width:10px; height:18px" ></span></span></span><span niloofar="" style="font-family:" xb="">&nbsp;را یک میدان پتانسیل برای این سالیتون هذلولوی گویند. در این مقاله، یک میدان برداری هندسی جدید معرفی می‌کنیم که علاوه بر آنکه در ارتباط با هندسه منیفلد مورد مطالعه است، هرگاه به عنوان یک میدان پتانسیل برای یک سالیتون هذلولوی در نظر گرفته شود به مفهوم سیال نسبیتی مرتبط شده و بنابراین، هندسه فضا-زمان و خواص موجی مترهای شبه-ریمانی را به هم مربوط می‌سازد. نهایتا، کاربردهای دیگر این ساختار را در منیفلدهای فضا-زمان جستجو می‌کنیم.&nbsp;</span></span> A hyperbolic Ricci soliton is ... سالیتون هذلولوی, منیفلد شبه-ریمانی, نسبیت عام Hyperbolic Ricci soliton, Semi-Riemannian manifold, General relativity. 18 30 http://mmr.khu.ac.ir/browse.php?a_code=A-10-454-5&slc_lang=fa&sid=1 Ghodratallah Fasihi-Ramandi قدرت اله فصیحی رامندی fasihi@sci.ikiu.ac.ir 10031947532846006927 10031947532846006927 Yes دانشگاه بین المللی امام خمینی Farzaneh Shamkhali فرزانه شمخالی shamkhali56@gmail.com 10031947532846006928 10031947532846006928 No دانشگاه بین المللی امام خمینی Shahroud Azami شاهرود اعظمی Azami@sci.ikiu.ac.ir 10031947532846006929 10031947532846006929 No دانشگاه بین المللی امام خمینی